This is pretty cool, and a non-obvious application of a Large Language Model. The only rough spots are those inherent in the LLM itself, for example for suggestions that incorporate "self storage" the results tended to waffle between interpreting it as online storage and physical storage facilities. Perhaps some hidden disambiguation could be added to the prompt.
I built a little-side project that tries to use GPT-3 to find and describe novel business ideas at the intersection of two existing projects. Was a fun little experiment to build so wanted to share it here :)
Hmm. Holding one category steady and checking the others invariably reveals a combination that hasn't been generated (like in dozens of tries I didn't get one pregenerated result), so you definitely need to figure out how to fund more prompt results.
One thing you could try is to treat this as a straightforward content farm and sell ads or sponsorship on the site. Using Google AdSense won't work since they prohibit machine generated content. You might be able to partner with a small ad network to explore specific slices of the combinatorial explosion (eg. "Pets" or "Food").
There is probably a lot you can do in terms of clever yield management such as cheaply pre-generating just the neologism or descriptive term (like, just four words) and checking to see whether it and/or the original terms reveal good search results and/or are being actively bid on through AdWords before you select which to generate the four full prompts for.
Allow users to upvote/downvote results such that disappointing ones should be shown less often or even regenerated if sufficiently unpopular. Possibly have the vote be on a specific prompt and its result rather than the entire set of four.
GPT has shown facility in determining when a prompt doesn't make sense, experimenting with that to better target your limited generation budget to "good" combinations may help:
Brainstorm some ideas combining Liqour Stores and healing modalities
-Liquor store/massage parlor: A place where people can go to get massages and purchase liquor.
-Liquor store/yoga studio: A place where people can purchase liquor and take yoga classes.
-Liquor store/spa: A place where people can purchase liquor and get spa treatments.
-Liquor store/gym: A place where people can purchase liquor and work out.